Finite Group Databasebeta

← Group #11722077

Character table — Group #11722077

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222222222222244444444444444444444444444444444444444444444181818181818181818181818363636363636363636363636
order12442333466666121212121212121233333666666666666666661212121212121212121212121212121212121212121244441212121212121212246688121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ511-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1-111i−i-1-1ii−i−i
χ611-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i-11-1-1−ii11−i−iii
χ711-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1-111−ii-1-1−i−iii
χ811-1-1-1111111-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii-11-1-1i−i11ii−i−i
χ92222222-122222-12222-1-1222-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000022-1-100-1-10000
χ102222222-122222-12222-1-1222-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000-2-21100110000
χ11222222-1222-1222222222-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000000002200-1-1-1-1
χ12222222-1222-1222222222-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000000000000000-2-2001111
χ1322222-1222-12-1-12-1-1-1-12222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ1422222-1222-12-1-12-1-1-1-12222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111000000000000
χ152222-2222-222-2-22-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-22222222222000000000000000000000000
χ162222-222-1-222-2-2-1-2-222-1-1222-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-100000000000000−i3i300−i3i30000
χ172222-222-1-222-2-2-1-2-222-1-1222-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-100000000000000i3−i300i3−i30000
χ182222-22-12-22-1-2-22-2-22222-1-1-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-100000000000000000000−i3i3−i3i3
χ192222-22-12-22-1-2-22-2-22222-1-1-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-100000000000000000000i3−i3i3−i3
χ202222-2-122-2-1211211-1-12222-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-1000033−3−333−3−3000000000000
χ212222-2-122-2-1211211-1-12222-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-10000−3−333−3−333000000000000
χ2222-2-22222-222222-2-2-2-2-2-2-2-22222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ2322-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-211111111-2-21111111100000000000000−i3i300i3−i30000
χ2422-2-2222-1-22222-1-2-2-2-211-2-22-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-211111111-2-21111111100000000000000i3−i300−i3i30000
χ2522-2-222-12-22-1222-2-2-2-2-2-211-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-11-211-2-211111111-2-2111111000000000000000000003−3−33
χ2622-2-222-12-22-1222-2-2-2-2-2-211-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-11-211-2-211111111-2-211111100000000000000000000−333−3
χ2722-2-22-122-2-12-1-121111-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-211111111-2-211110000−i3−i3i3i3i3i3−i3−i3000000000000
χ2822-2-22-122-2-12-1-121111-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-2-21111-2-211111111-2-211110000i3i3−i3−i3−i3−i3i3i3000000000000
χ2922-2-2-222-1222-2-2-122-2-211-2-22-1-1-1-1-21-2-2111111112-1-1-1-12-122-1-1-1-1-1-1-1-1-2-2111111110000000000002-2-1-100110000
χ3022-2-2-222-1222-2-2-122-2-211-2-22-1-1-1-1-21-2-2111111112-1-1-1-12-122-1-1-1-1-1-1-1-1-2-211111111000000000000-221100-1-10000
χ3122-2-2-22-1222-1-2-2222-2-2-2-211-12-1-1-11-211-2-2111111-12-1-1-1-12-1-122-1-1-1-1-1-111-2-211111100000000000000002i−2i00−i−iii
χ3222-2-2-22-1222-1-2-2222-2-2-2-211-12-1-1-11-211-2-2111111-12-1-1-1-12-1-122-1-1-1-1-1-111-2-21111110000000000000000−2i2i00ii−i−i
χ3322-2-2-2-1222-12112-1-111-2-2-2-2-1-12-1-1-2-21111-2-21111-1-12-1-122-1-1-1-122-1-1-1-11111-2-211112i2i−2i−2i−i−i−i−iiiii000000000000
χ3422-2-2-2-1222-12112-1-111-2-2-2-2-1-12-1-1-2-21111-2-21111-1-12-1-122-1-1-1-122-1-1-1-11111-2-21111−2i−2i2i2iiiii−i−i−i−i000000000000
χ352-22i−2i02220-2-200-2002i−2i2i−2i2i−2i22222000000000000-2-2-2-2-20000000000002i−2i2i−2i2i−2i2i2i−2i−2i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ362-22i−2i02220-2-200-2002i−2i2i−2i2i−2i22222000000000000-2-2-2-2-20000000000002i−2i2i−2i2i−2i2i2i−2i−2i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ372-22i−2i0-12201-2−i3i3-23−3−ii2i−2i2i−2i-1-12-1-100−i3i3−i3i300−i3−i3i3i311-211003−33−30033−3−3−ii−ii2i−2i−i−iii1+i−1−i1−i−1+i−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7000000000000
χ382-22i−2i0-12201-2−i3i3-23−3−ii2i−2i2i−2i-1-12-1-100−i3i3−i3i300−i3−i3i3i311-211003−33−30033−3−3−ii−ii2i−2i−i−iii−1−i1+i−1+i1−iζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11ζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7000000000000
χ392-22i−2i0-12201-2i3−i3-2−33−ii2i−2i2i−2i-1-12-1-100i3−i3i3−i300i3i3−i3−i311-21100−33−3300−3−333−ii−ii2i−2i−i−iii1+i−1−i1−i−1+i−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11000000000000
χ402-22i−2i0-12201-2i3−i3-2−33−ii2i−2i2i−2i-1-12-1-100i3−i3i3−i300i3i3−i3−i311-21100−33−3300−3−333−ii−ii2i−2i−i−iii−1−i1+i−1+i1−iζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7ζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11000000000000
χ412-2−2i2i02220-2-200-200−2i2i−2i2i−2i2i22222000000000000-2-2-2-2-2000000000000−2i2i−2i2i−2i2i−2i−2i2i2i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ422-2−2i2i02220-2-200-200−2i2i−2i2i−2i2i22222000000000000-2-2-2-2-2000000000000−2i2i−2i2i−2i2i−2i−2i2i2i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ432-2−2i2i0-12201-2−i3i3-2−33i−i−2i2i−2i2i-1-12-1-100−i3i3−i3i300−i3−i3i3i311-21100−33−3300−3−333i−ii−i−2i2iii−i−i1−i−1+i1+i−1−i−ζ2−ζ7ζ2+ζ7−ζ10−ζ11ζ10+ζ11−ζ10+ζ11ζ10−ζ11−ζ2+ζ7ζ2−ζ7000000000000
χ442-2−2i2i0-12201-2−i3i3-2−33i−i−2i2i−2i2i-1-12-1-100−i3i3−i3i300−i3−i3i3i311-21100−33−3300−3−333i−ii−i−2i2iii−i−i−1+i1−i−1−i1+iζ2+ζ7−ζ2−ζ7ζ10+ζ11−ζ10−ζ11ζ10−ζ11−ζ10+ζ11ζ2−ζ7−ζ2+ζ7000000000000
χ452-2−2i2i0-12201-2i3−i3-23−3i−i−2i2i−2i2i-1-12-1-100i3−i3i3−i300i3i3−i3−i311-211003−33−30033−3−3i−ii−i−2i2iii−i−i1−i−1+i1+i−1−i−ζ10−ζ11ζ10+ζ11−ζ2−ζ7ζ2+ζ7−ζ2+ζ7ζ2−ζ7−ζ10+ζ11ζ10−ζ11000000000000
χ462-2−2i2i0-12201-2i3−i3-23−3i−i−2i2i−2i2i-1-12-1-100i3−i3i3−i300i3i3−i3−i311-211003−33−30033−3−3i−ii−i−2i2iii−i−i−1+i1−i−1−i1+iζ10+ζ11−ζ10−ζ11ζ2+ζ7−ζ2−ζ7ζ2−ζ7−ζ2+ζ7ζ10−ζ11−ζ10+ζ11000000000000
χ47444444-2-244-244-24444-2-2-2-2-2-2111-2-2-2-2-2-2111111-2-2111-2-2-2-2-2-2111111-2-2-2-2111111000000000000000000000000
χ4844444-24-24-24-2-2-2-2-2-2-2-2-244-21-2114-2-2-211-2-21111-21-2114-2-2-211-2-21111-2-211-2-21111000000000000000000000000
χ4944444-2-244-2-2-2-24-2-2-2-244-2-21-2-211-2411-2-2-2-211111-2-211-2411-2-2-2-2111111-2-2-2-21111000000000000000000000000
χ5044444-2-2-24-2-2-2-2-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000
χ5144444-2-2-24-2-2-2-2-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000
χ524444-44-2-2-44-2-4-4-2-4-444-2-2-2-2-2-2111222222-1-1-1-1-1-1-2-2111222222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000
χ534444-4-24-2-4-2422-222-2-2-2-244-21-211-4222-1-122-1-1-1-1-21-211-4222-1-122-1-1-1-1-2-211-2-21111000000000000000000000000
χ544444-4-2-24-4-2-222422-2-244-2-21-2-2112-4-1-12222-1-1-1-11-2-2112-4-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000
χ554444-4-2-2-2-4-2-222-222-2-2-2-2-2-2111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000
χ564444-4-2-2-2-4-2-222-222-2-2-2-2-2-2111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000
χ5744-4-444-2-2-44-244-2-4-4-4-42222-2-2111-2-2-2-2-2-2111111-2-2111222222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000
χ5844-4-44-24-2-4-24-2-2-2222222-4-4-21-2114-2-2-211-2-21111-21-211-4222-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000
χ5944-4-44-2-24-4-2-2-2-242222-4-4221-2-211-2411-2-2-2-211111-2-2112-4-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000
χ6044-4-44-2-2-2-4-2-2-2-2-222222222111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000
χ6144-4-44-2-2-2-4-2-2-2-2-222222222111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000
χ6244-4-4-44-2-244-2-4-4-244-4-42222-2-2111222222-1-1-1-1-1-1-2-2111-2-2-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000
χ6344-4-4-4-24-24-2422-2-2-22222-4-4-21-211-4222-1-122-1-1-1-1-21-2114-2-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000
χ6444-4-4-4-2-244-2-2224-2-222-4-4221-2-2112-4-1-12222-1-1-1-11-2-211-2411-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000
χ6544-4-4-4-2-2-24-2-222-2-2-2222222111−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000
χ6644-4-4-4-2-2-24-2-222-2-2-2222222111−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000
χ674-44i−4i044-20-4-4002004i−4i−2i2i4i−4i4-2-2-2-2000000000000-422220000000000004i−4i−2i2i−2i2i−2i−2i2i2i000000000000000000000000
χ684-44i−4i04-240-4200-4004i−4i4i−4i−2i2i-24-2-2-20000000000002-4222000000000000−2i2i4i−4i−2i2i−2i−2i2i2i000000000000000000000000
χ694-44i−4i04-2-20-42002004i−4i−2i2i−2i2i-2-21110000003-33-3-3322-1-1-10000003i−3i3i−3i−3i3i−2i2i−2i2ii−iii−i−i000000000000000000000000
χ704-44i−4i04-2-20-42002004i−4i−2i2i−2i2i-2-2111000000-33-333-322-1-1-1000000−3i3i−3i3i3i−3i−2i2i−2i2ii−iii−i−i000000000000000000000000
χ714-44i−4i0-24-202-4−2i32i3223−23−2i2i−2i2i4i−4i-21-21100−2i32i3i3−i300i3i3−i3−i32-12-1-10023−23−3300−3−333−2i2ii−i−2i2iii−i−i000000000000000000000000
χ724-44i−4i0-24-202-42i3−2i32−2323−2i2i−2i2i4i−4i-21-211002i3−2i3−i3i300−i3−i3i3i32-12-1-100−23233−30033−3−3−2i2ii−i−2i2iii−i−i000000000000000000000000
χ734-44i−4i0-2-24022−2i32i3-423−23−2i2i4i−4i−2i2i1-2-21100i3−i3−2i32i300i3i3−i3−i3-122-1-100−3323−2300−3−333i−i−2i2i−2i2iii−i−i000000000000000000000000
χ744-44i−4i0-2-240222i3−2i3-4−2323−2i2i4i−4i−2i2i1-2-21100−i3i32i3−2i300−i3−i3i3i3-122-1-1003−3−23230033−3−3i−i−2i2i−2i2iii−i−i000000000000000000000000
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χ764-44i−4i0-2-2-2022−2i32i3223−23−2i2i−2i2i−2i2i111−1+3i32−1−3i3200i3−i3i3−i3-333−i32−3−i32−3+i323+i32-1-1-11−3i321+3i3200−33−33−3i3i−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11i−ii−ii−i2ζ7−ζ11−ζ7+2ζ11−2ζ7+ζ11ζ7−2ζ11000000000000000000000000
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χ894-4−4i4i0-2-2-20222i3−2i3223−232i−2i2i−2i2i−2i111−1−3i32−1+3i3200−i3i3−i3i3-333+i32−3+i32−3−i323−i32-1-1-11+3i321−3i3200−33−333i−3iζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ11−ii−ii−iiζ7−2ζ11−2ζ7+ζ11−ζ7+2ζ112ζ7−ζ11000000000000000000000000
χ904-4−4i4i0-2-2-20222i3−2i3223−232i−2i2i−2i2i−2i111−1+3i32−1−3i3200−i3i3−i3i33-3−3+i323+i323−i32−3−i32-1-1-11−3i321+3i3200−33−33−3i3i−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11−ii−ii−ii−2ζ7+ζ11ζ7−2ζ112ζ7−ζ11−ζ7+2ζ11000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.